The second picture shows the relation between two objects. The car belongs to the man who is right next to the door. The possessing of something is described with the Genitive. In English the Genitive is formed with a preposition.

das Auto des Mannes = the car of the man

The German language uses a declination not a preposition:

article noun preposition article noun   das   Haus   -   der   Frau   the   house   of   the   woman

Since the Germans don't use a preposition, they have to have another way of noticing what kind of relation is between the woman and the house. Have a look at the definite articles:

das Haus der Frau it is der Frau in Genitive not die Frau (like in basic form) This der Frau corresponds to of the woman

We have to admit that the English system is much easier as the table below shows. However there is nothing we can do to make it easier.

declination in German and the English system

das Haus - der Frau Nominative: die Frau Genitive: der Frau   the house of the woman preposition de   das Haus - der Frauen Nominative: die Frauen Genitive: der Frauen   the house of the women preposition de   das Haus - des Mannes Nominative: der Mann Genitive: des Mannes   the house of the man preposition of   das Haus - der Männer Nominative: die Männer Genitive: der Männer   the house of the men preposition of   das Haus - des Kindes Nominative: das Kind Genitive: des Kindes   the house of the child preposition of   das Haus - der Kinder Nominative: die Kinder Genitive: der Kinder   the house of the children preposition of

For the object in Genitive you ask: Whose? or Of which?